Adjective

In answer to your question "What do you call a person who doesn't like questions being asked?", I think of such a person as an authoritarian, self-important, fascist, close-minded, stupid, supercilious, cross-grained, arrogant and imperious fool, dunderhead, or dictator.

But perhaps that's not what you want to know, and perhaps meant to ask, "How should [Maureen] refer to this question-averse aspect of her sister?", which of course I don't know. However, if previously-suggested shy, silent, private and secretive don't apply, also consider veiled, introverted, taciturn, censorial, no-nonsense, thin-skinned, touchy and untalkative.

Based on analysis of Gardner's multiple intelligences, the faculties of the mind and the characteristics suggestive of the learning disabled: adding inattentiveness or inadvertance, bodily or mindfully impaired and/or lost, visually or aurally illiterate, unfocused, corrupt, unreasonable to be a fool! However, the summarized fool is based off memory and attention issues. He may not like other conversational circumstances. If he doesn't like conversational circumstances entirely he is sociolinguistically (conversationally) incompetent, Noam Chomsky might say. The person who doesn't like answering questions in the worst case would be a fool. This question has helped me to see that incompetence, impairment, mindlessness, illiteracy and foolishness can be a rolling problem. It's only rolling if the worst case scenario fool has memory and attention problems, and the rest aforementioned. Thanks for helping me study for the Praxis PLT with this archetype!